## Abstract

We consider decay of metastable topological configurations such as strings and domain walls. The transition from a state with higher energy density to a state with lower one proceeds through quantum tunneling or through thermally catalyzed quantum tunneling (at sufficiently small temperatures). The transition rate is calculated at zero temperature including the preexponential factor and also at a finite low temperature. The thermal enhancement factor is closely related to the probability (effective length) of destruction of the string (the domain wall) in collisions of the Goldstone bosons, corresponding to transverse waves on the string (wall). We derive a general formula which allows to find the probability (effective length) of a string (wall) breakup by a collision of arbitrary number of the bosons. We find that the destruction of a string only takes place in collisions of even number of the bosons, while the destruction of the wall can occur in a collision of any number of particles. We explicitly calculate the energy dependence of such processes in two-particle collisions for arbitrary relation between the energy and the largest infrared scale (the size of a critical gap).

Original language | English (US) |
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Pages (from-to) | 16-48 |

Number of pages | 33 |

Journal | Annals of Physics |

Volume | 325 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2010 |

### Bibliographical note

Funding Information:This work is supported in part by the DOE Grant DE-FG02-94ER40823. The work of A.M. is also supported in part by the RFBR Grant No. 07-02-00878 and by the Scientific School Grant No. NSh-3036.2008.2.

## Keywords

- Metastable domain wall
- Metastable string
- Tunneling